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    <title>proj</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>proj</b> -  projection</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>P = proj(X1,X2)    </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>X1,X2</b>
        </tt>: two real matrices with equal number of columns</li>
      <li>
        <tt>
          <b>P</b>
        </tt>: real projection matrix (<tt>
          <b>P^2=P</b>
        </tt>)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>P</b>
      </tt> is the projection on <tt>
        <b>X2</b>
      </tt> parallel to <tt>
        <b>X1</b>
      </tt>.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

X1=rand(5,2);X2=rand(5,3);
P=proj(X1,X2);
norm(P^2-P,1)
trace(P)    // This is dim(X2)
[Q,M]=fullrf(P);
svd([Q,X2])   // span(Q) = span(X2)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="projspec.htm">
        <tt>
          <b>projspec</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="orth.htm">
        <tt>
          <b>orth</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="fullrf.htm">
        <tt>
          <b>fullrf</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F. D.; ;   </p>
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